This paper addresses two issues that concern the electricity market participants under the European day-ahead market (DAM) framework, namely the feasibility of the attained schedules and the non-confiscation of cleared volumes. To address the first issue, new resource-specific orders, i.e., thermal orders for thermal generating units, demand response orders for load responsive resources, and energy limited orders for storage resources, are proposed and incorporated in the existing European DAM clearing problem. To address the second issue, two approaches which lead to a non-confiscatory market are analyzed① discriminatory pricing with side-payments (U.S. paradigm); and ② non-discriminatory pricing excluding out-of-money orders (European paradigm). A comparison is performed between the two approaches to investigate the most appropriate pricing rule in terms of social welfare, derived revenues for the sellers, and efficiency of the attained results. The proposed model with new resource-specific products is evaluated in a European test system, achieving robust solutions. The feasibility of the attained schedules is demonstrated when using resource-specific orders compared with block orders. Finally, the results indicate the supremacy of discriminatory pricing with side-payments compared with the current European pricing rule.